作业帮已知数列{a}的通项公式为an=48/[(n+2)^2-4],Sn是它的前n项和,则与S98最接近的整数是20,21,24还是25?
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![已知数列{a}的通项公式为an=48/[(n+2)^2-4],Sn是它的前n项和,则与S98最接近的整数是20,21,24还是25?](/uploads/image/z/14712333-69-3.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ba%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E4%B8%BAan%3D48%2F%5B%28n%2B2%29%5E2-4%5D%2CSn%E6%98%AF%E5%AE%83%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C%E5%88%99%E4%B8%8ES98%E6%9C%80%E6%8E%A5%E8%BF%91%E7%9A%84%E6%95%B4%E6%95%B0%E6%98%AF20%2C21%2C24%E8%BF%98%E6%98%AF25%3F)
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已知数列{a}的通项公式为an=48/[(n+2)^2-4],Sn是它的前n项和,则与S98最接近的整数是20,21,24还是25?
已知数列{a}的通项公式为an=48/[(n+2)^2-4],Sn是它的前n项和,则与S98最接近的整数是20,21,24还是25?
已知数列{a}的通项公式为an=48/[(n+2)^2-4],Sn是它的前n项和,则与S98最接近的整数是20,21,24还是25?
an=48/[(n+2)^2-4]
=48/[(n+2+2)(n+2-2)]
=48/(n*(n+4))
=12*[1/n-1/(n+4)]
Sn=12*(1-1/5+1/2-1/6+1/3-1/7+1/4-1/8+1/5-1/9+...+1/(n-4)-1/n+1/(n-3)-1/(n+1)+1/(n-2)-1/(n+2)+1/(n-1)-1/(n+3)+1/n-1/(n+4))
Sn=12*[1+1/2+1/3+1/4-1/(n+1)-1/(n+2)-1/(n+3)-1/(n+4)]
=12+6+4+3-12*[1/(n+1)+1/(n+2)+1/(n+3)+1/(n+4)]
=25-12*[1/(n+1)+1/(n+2)+1/(n+3)+1/(n+4)]
S98=25-12*(1/99+1/100+1/101+1/102)
>25-12*(1/99+1/99+1/99+1/99)
=25-48/99
>25-48/96
=24.5
S98>24.5
S98最接近的整数是 25